Cascading failure dynamics driven by nonlinear capacity allocation in multilayer networks

In multilayer complex networks, localized disruptions may trigger abrupt system-level breakdowns, thereby inducing cascading failures. This phenomenon is primarily governed by the nonlinear interactions among node load, capacity allocation, and network structure. To investigate the cascading dynamics induced by a nonlinear load-capacity model in a practical setting, this study develops a metro-bus double-layer network (M-B DLN) framework based on a real-world interdependent metro-bus system. In this framework, node capacity is defined as a nonlinear function of load, regulated by a capacity adjustment parameter (α) and a structural sensitivity parameter (β). Cascading processes are simulated through a dynamic load redistribution mechanism with a two-step transfer constraint, reflecting realistic limits on flow reallocation. Moreover, four key metrics, largest connected component (LCC), average path length (APL), global network efficiency (GNE), and loss ratio (R), are introduced to evaluate the network robustness. The results reveal that α delays the collapse of the critical round by increasing system redundancy, while β controls the onset and progression of phase transitions. Furthermore, the various attack experiments indicate that cascading dynamics are primarily governed by network structure and nonlinear load-capacity interactions, and relaxing transfer constraints delays failure propagation with a diminishing marginal effect. These findings highlight how nonlinear load-capacity reshapes cascading failure patterns in multilayer systems and provide insights into the interactions among node load, capacity allocation, and structure in complex networks.